Letters in Mathematical Physics最新文献_第8页

The intertwined derivative Schrödinger system of Calogero–Moser–Sutherland type 卡洛吉罗-莫瑟-萨瑟兰型交织导数薛定谔系统

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-03 DOI: 10.1007/s11005-024-01815-x

Ruoci Sun

{"title":"The intertwined derivative Schrödinger system of Calogero–Moser–Sutherland type","authors":"Ruoci Sun","doi":"10.1007/s11005-024-01815-x","DOIUrl":"10.1007/s11005-024-01815-x","url":null,"abstract":"<div><p>This paper is dedicated to extending the focusing/defocusing Calogero–Moser–Sutherland cubic derivative Schrödinger equations (CMSdNLS) </p><div><div><span>$$begin{aligned} small ipartial _t u + partial _x^2 u = pm u left( textrm{D} + |textrm{D}| right) left( |u|^2 right) , quad textrm{D}= -ipartial _x, quad x in mathbb {R} quad textrm{or} quad x in mathbb {T}:= mathbb {R}/2 pi mathbb {Z}, end{aligned}$$</span></div></div><p>which were initially introduced in Matsuno (Phys Lett A 278(1–2):53–58, 2000; Inverse Probl 18:1101–1125, 2002; J Phys Soc Jpn 71(6):1415–1418, 2002; Inverse Prob 20(2):437–445, 2004), Abanov et al. (J Phys A 42(13): 135201, 2009), Gérard and Lenzmann (The Calogero–Moser derivative nonlinear Schrödinger equation, Communications on Pure and Applied Mathematics. arXiv:2208.04105) and Badreddine (On the global well-posedness of the Calogero–Sutherland derivative nonlinear Schrödinger equation, Pure and Applied Analysis. arXiv:2303.01087; Traveling waves and finite gap potentials for the Calogero–Sutherland derivative nonlinear Schrödinger equation, Annales de l’Institut Henri Poincaré, Analyse Non Linéaire. arXiv:2307.01592), to a system of two matrix-valued variables, leading to the following intertwined system, </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} ipartial _t U + partial _x^2 U = - tfrac{1}{2} U left( textrm{D} + |textrm{D}| right) left( V^* Uright) - tfrac{1}{2} V left( textrm{D} + |textrm{D}| right) left( U^* Uright) , ipartial _t V + partial _x^2 V = - tfrac{1}{2} V left( textrm{D} + |textrm{D}| right) left( U^* Vright) - tfrac{1}{2} U left( textrm{D} + |textrm{D}| right) left( V^* Vright) . end{array}right. } end{aligned}$$</span></div></div><p>This system enjoys a Lax pair structure, enabling the establishment of an explicit formula for general solutions on both the 1-dimensional torus and the real line. Consequently, this system can be regarded as an integrable perturbation and extension of both the linear Schrödinger equation and the CMSdNLS equations.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lorentzian metric spaces and their Gromov–Hausdorff convergence 洛伦兹度量空间及其格罗莫夫-豪斯多夫收敛性

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-29 DOI: 10.1007/s11005-024-01813-z

E. Minguzzi, S. Suhr

{"title":"Lorentzian metric spaces and their Gromov–Hausdorff convergence","authors":"E. Minguzzi, S. Suhr","doi":"10.1007/s11005-024-01813-z","DOIUrl":"10.1007/s11005-024-01813-z","url":null,"abstract":"<div><p>We present an abstract approach to Lorentzian Gromov–Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary “positive signature” metrics or other unobserved fields. We begin by defining a notion of (abstract) bounded Lorentzian metric space which is sufficiently general to comprise compact causally convex subsets of globally hyperbolic spacetimes and causets. We define the Gromov–Hausdorff distance and show that two bounded Lorentzian metric spaces at zero GH distance are indeed both isometric and homeomorphic. Then we show how to define from the Lorentzian distance, beside topology, the causal relation and the causal curves for these spaces, obtaining useful limit curve theorems. Next, we define Lorentzian (length) prelength spaces via suitable (maximal) chronal connectedness properties. These definitions are proved to be stable under GH limits. Furthermore, we define bounds on sectional curvature for our Lorentzian length spaces and prove that they are also stable under GH limits. We conclude with a (pre)compactness theorem.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01813-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Geometric Dirac operator on noncommutative torus and (M_2({mathbb {C}})) 非交换环上的几何狄拉克算子和 $$M_2({mathbb {C}})$$

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-28 DOI: 10.1007/s11005-024-01806-y

E. Lira-Torres, S. Majid

{"title":"Geometric Dirac operator on noncommutative torus and (M_2({mathbb {C}}))","authors":"E. Lira-Torres, S. Majid","doi":"10.1007/s11005-024-01806-y","DOIUrl":"10.1007/s11005-024-01806-y","url":null,"abstract":"<div><p>We solve for quantum geometrically realised pre-spectral triples or ‘Dirac operators’ on the noncommutative torus <span>({mathbb {C}}_theta [T^2])</span> and on the algebra <span>(M_2({mathbb {C}}))</span> of <span>(2times 2)</span> matrices with their standard quantum metrics and associated quantum Riemannian geometry. For <span>({mathbb {C}}_theta [T^2])</span>, we obtain a standard even spectral triple but now uniquely determined by full geometric realisability. For <span>(M_2({mathbb {C}}))</span>, we are forced to a particular flat quantum Levi-Civita connection and again obtain a natural fully geometrically realised even spectral triple. In both cases there is an odd spectral triple for a different choice of a sign parameter. We also consider an alternate quantum metric on <span>(M_2({mathbb {C}}))</span> with curved quantum Levi-Civita connection and find a natural 2-parameter family of Dirac operators which are almost spectral triples, where <img> fails to be antihermitian. In all cases, we split the construction into a local tensorial level related to the quantum Riemannian geometry, where we classify the results more broadly, and the further requirements relating to the pre-Hilbert space structure. We also illustrate the Lichnerowicz formula for <img> which applies in the case of a full geometric realisation.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01806-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Volume singularities in general relativity 广义相对论中的体积奇点

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-28 DOI: 10.1007/s11005-024-01814-y

Leonardo García-Heveling

引用次数: 0

Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties 闵科夫斯基时空考奇面上的量子粒子局域化观测值及其因果特性

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-28 DOI: 10.1007/s11005-024-01817-9

Carmine De Rosa, Valter Moretti

{"title":"Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties","authors":"Carmine De Rosa, Valter Moretti","doi":"10.1007/s11005-024-01817-9","DOIUrl":"10.1007/s11005-024-01817-9","url":null,"abstract":"<div><p>We introduce and study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of a coherent family of normalized POVMs, one for each said Cauchy surface. We prove that a family of POVMs of this type automatically satisfies a causality condition which generalizes Castrigiano’s one and implies it when restricting to flat spacelike Cauchy surfaces. As a consequence, no conflict with Hegerfeldt’s theorem arises. We furthermore prove that such families of POVMs do exist for massive Klein–Gordon particles, since some of them are extensions of already known spatial localization observables. These are constructed out of positive definite kernels or are defined in terms of the stress–energy tensor operator. Some further features of these structures are investigated, in particular the relation with the triple of Newton–Wigner selfadjoint operators and a modified form of Heisenberg inequality in the rest 3-spaces of Minkowski reference frames.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01817-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The genus two G-function for cubic elliptic orbifold and modularity 立方椭圆球面的属二 G 函数与模块性

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-27 DOI: 10.1007/s11005-024-01818-8

Xin Wang

引用次数: 0

Higher-order reductions of the Mikhalev system 米哈列夫系统的高阶还原

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-26 DOI: 10.1007/s11005-024-01811-1

E. V. Ferapontov, V. S. Novikov, I. Roustemoglou

{"title":"Higher-order reductions of the Mikhalev system","authors":"E. V. Ferapontov, V. S. Novikov, I. Roustemoglou","doi":"10.1007/s11005-024-01811-1","DOIUrl":"10.1007/s11005-024-01811-1","url":null,"abstract":"<div><p>We consider the 3D Mikhalev system, </p><div><div><span>$$ u_t=w_x, quad u_y= w_t-u w_x+w u_x, $$</span></div></div><p>which has first appeared in the context of KdV-type hierarchies. Under the reduction <span>(w=f(u))</span>, one obtains a pair of commuting first-order equations, </p><div><div><span>$$ u_t=f'u_x, quad u_y=(f'^2-uf'+f)u_x, $$</span></div></div><p>which govern simple wave solutions of the Mikhalev system. In this paper we study <i>higher-order</i> reductions of the form </p><div><div><span>$$ w=f(u)+epsilon a(u)u_x+epsilon ^2[b_1(u)u_{xx}+b_2(u)u_x^2]+cdots , $$</span></div></div><p>which turn the Mikhalev system into a pair of commuting higher-order equations. Here the terms at <span>(epsilon ^n)</span> are assumed to be differential polynomials of degree <i>n</i> in the <i>x</i>-derivatives of <i>u</i>. We will view <i>w</i> as an (infinite) formal series in the deformation parameter <span>(epsilon )</span>. It turns out that for such a reduction to be non-trivial, the function <i>f</i>(<i>u</i>) must be quadratic, <span>(f(u)=lambda u^2)</span>, furthermore, the value of the parameter <span>(lambda )</span> (which has a natural interpretation as an eigenvalue of a certain second-order operator acting on an infinite jet space), is quantised. There are only two positive allowed eigenvalues, <span>(lambda =1)</span> and <span>(lambda =3/2)</span>, as well as infinitely many negative rational eigenvalues. Two-component reductions of the Mikhalev system are also discussed. We emphasise that the existence of higher-order reductions of this kind is a reflection of <i>linear degeneracy</i> of the Mikhalev system, in particular, such reductions do not exist for most of the known 3D dispersionless integrable systems such as the dispersionless KP and Toda equations.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01811-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dimensional reduction formulae for spectral traces and Casimir energies 谱迹和卡西米尔能量的降维公式

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1007/s11005-024-01812-0

Alexander Strohmaier

引用次数: 0

Fermionic construction of the (frac{{mathbb Z}}{2})-graded meromorphic open-string vertex algebra and its ({mathbb Z}_2)-twisted module, II $$frac{mathbb Z}}{2}$$级联美态开弦顶点代数及其$${mathbb Z}_2$$扭曲模块的费米子构造, II

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1007/s11005-024-01795-y

Fei Qi

{"title":"Fermionic construction of the (frac{{mathbb Z}}{2})-graded meromorphic open-string vertex algebra and its ({mathbb Z}_2)-twisted module, II","authors":"Fei Qi","doi":"10.1007/s11005-024-01795-y","DOIUrl":"10.1007/s11005-024-01795-y","url":null,"abstract":"<div><p>This paper continues with Part I. We define the module for a <span>(frac{{mathbb Z}}{2})</span>-graded meromorphic open-string vertex algebra that is twisted by an involution and show that the axioms are sufficient to guarantee the convergence of products and iterates of any number of vertex operators. A module twisted by the parity involution is called a canonically <span>({mathbb Z}_2)</span>-twisted module. As an example, we give a fermionic construction of the canonically <span>({mathbb Z}_2)</span>-twisted module for the <span>(frac{{mathbb Z}}{2})</span>-graded meromorphic open-string vertex algebra constructed in Part I. Similar to the situation in Part I, the example is also built on a universal <span>({mathbb Z})</span>-graded non-anti-commutative Fock space where a creation operator and an annihilation operator satisfy the fermionic anti-commutativity relation, while no relations exist among the creation operators or among the zero modes. The Wick’s theorem still holds, though the actual vertex operator needs to be corrected from the naïve definition by normal ordering using the <span>(exp (Delta (x)))</span>-operator in Part I.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The spectral determinant for second-order elliptic operators on the real line 实线上二阶椭圆算子的谱行列式

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-23 DOI: 10.1007/s11005-024-01819-7

Pedro Freitas, Jiří Lipovský

引用次数: 0